feat(battle-node): thread MatchContext through bridge to BattleSession

IMatchingBridge.RegisterPendingBattle now takes a MatchContext; PendingBattle
carries it; BattleSession stores it. ArenaTwoPickBattleController builds ctx
from IMatchContextBuilder. ScriptedLifecycle still uses ScriptedProfiles for
the player half — Tasks 5/6 migrate the lifecycle.

Existing tests updated: MatchingBridgeTests, BattleNodeFlowTests,
InMemoryBattleSessionStoreTests, BattleSessionDispatchTests, BattleSession
PumpTests, ArenaTwoPickBattleControllerTests (which now seeds a TK2 run +
adds a no-active-run 400 case).

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

SVSim.BattleNode/Sessions/BattleSession.cs

@@ -2,6 +2,7 @@ using System.Net.WebSockets;
 using System.Security.Cryptography;
 using System.Text;
 using Microsoft.Extensions.Logging;
+using SVSim.BattleNode.Bridge;
 using SVSim.BattleNode.Lifecycle;
 using SVSim.BattleNode.Protocol;
 using SVSim.BattleNode.Protocol.Bodies;
@@ -37,12 +38,19 @@ public sealed class BattleSession
     public InboundTracker Inbound { get; } = new();
     public OutboundSequencer Outbound { get; } = new();
 
-    public BattleSession(WebSocket ws, string battleId, long viewerId, ILogger<BattleSession> log)
+    /// <summary>
+    /// Player-side snapshot captured at do_matching time. ScriptedLifecycle reads the player
+    /// half of Matched/BattleStart frames from here; opponent half stays in ScriptedProfiles.
+    /// </summary>
+    internal MatchContext Context { get; }
+
+    public BattleSession(WebSocket ws, string battleId, long viewerId, MatchContext context, ILogger<BattleSession> log)
     {
         _ws = ws;
         _log = log;
         BattleId = battleId;
         ViewerId = viewerId;
+        Context = context;
     }
 
     /// <summary>